The sum (resp. the sum of squares) of the defects in the triangle inequalities for the area one lattice parallelograms in the first quadrant has a surprisingly simple expression. Namely, let f(a,b,c,d)=a2+b2+c2+d2-(a+c)2+(b+d)2. Then, [Figure not available: see fulltext.][Figure not available: see fulltext.] where the sum runs by all a, b, c, d∈ Z_{≥ 0} such that ad- bc= 1. We present a proof of these formulae and list several directions for the future studies.